Problem: Nauuo is a girl who loves playing chess.

One day she invented a game by herself which needs n chess pieces to play on a m× m chessboard. The rows and columns are numbered from 1 to m. We denote a cell on the intersection of the r-th row and c-th column as (r,c).

The game's goal is to place n chess pieces numbered from 1 to n on the chessboard, the i-th piece lies on (r_i,\,c_i), while the following rule is satisfied: for all pairs of pieces i and j, |r_i-r_j|+|c_i-c_j|≥|i-j|. Here |x| means the absolute value of x.

However, Nauuo discovered that sometimes she couldn't find a solution because the chessboard was too small.

She wants to find the smallest chessboard on which she can put n pieces according to the rules.

She also wonders how to place the pieces on such a chessboard. Can you help her?

Input

The only line contains a single integer n (1≤ n≤ 1000) — the number of chess pieces for the game.

Output

The first line contains a single integer — the minimum value of m, where m is the length of sides of the suitable chessboard.

The i-th of the next n lines contains two integers r_i and c_i (1≤ r_i,c_i≤ m) — the coordinates of the i-th chess piece.

If there are multiple answers, print any.

Examples

Input


2


Output


2
1 1
1 2

Input


4


Output


3
1 1
1 3
3 1
3 3

Note

In the first example, you can't place the two pieces on a 1×1 chessboard without breaking the rule. But you can place two pieces on a 2×2 chessboard like this:

<image>

In the second example, you can't place four pieces on a 2×2 chessboard without breaking the rule. For example, if you place the pieces like this:

<image>

then |r_1-r_3|+|c_1-c_3|=|1-2|+|1-1|=1, |1-3|=2, 1<2; and |r_1-r_4|+|c_1-c_4|=|1-2|+|1-2|=2, |1-4|=3, 2<3. It doesn't satisfy the rule.

However, on a 3×3 chessboard, you can place four pieces like this:

<image>

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;
import java.lang.*;

public final class Solution {

    void solve() throws java.lang.Exception {
        int n = ri();
        int m = n/2 + 1;
        wr(m); wl();
        for (int i=1; i<=m; i++) {
            wr("1 " + i);
            wl();
        }
        for (int i=2; i<=n-m+1; i++) {
            wr(i + " " + m);
            wl();
        }
    }

    public static void main(String[] args) throws java.lang.Exception {
        Reader reader = null;
        Writer writer = null;
        try {
            if (System.getProperty("ONLINE_JUDGE") == null) {
                reader = new Reader(new FileInputStream("input.txt"));
                writer = new Writer(new FileOutputStream("output.txt"));
            } else {
                reader = new Reader(System.in);
                writer = new Writer(System.out);
            }            
            new Solution(reader, writer).solve();
        } finally {
            if (reader != null)
                reader.close();
            if (writer != null)
                writer.close();
        }
    }

    Reader reader;
    Writer writer;

    Solution(Reader reader, Writer writer) {
        this.reader = reader;
        this.writer = writer;
    }

    int ri() throws java.lang.Exception {
        return reader.nextInt();
    }

    int[] ria() throws java.lang.Exception {
        int n = ri();
        int[] a = new int[n];
        for (int i=0; i<n; i++) a[i] = ri();
        return a;
    }

    long rl() throws java.lang.Exception {
        return reader.nextLong();
    }

    long[] rla() throws java.lang.Exception {
        int n = ri();
        long[] a = new long[n];
        for (int i=0; i<n; i++) a[i] = rl();
        return a;
    }

    double rd() throws java.lang.Exception {
        return reader.nextDouble();
    }

    String rs() {
        return reader.nextToken();
    }

    String rline()  throws java.lang.Exception {
        return reader.nextLine();
    }

    void wr(int x)  throws java.lang.Exception {
        writer.write(x);
    }

    void wr(int[] a)  throws java.lang.Exception {
        for (int i=0; i<a.length; i++) {
            if (i!=0) wr(" ");
            wr(a[i]);
        }
        wl();
    }

    void wr(long x)  throws java.lang.Exception {
        writer.write(x);
    }

    void wr(long[] a)  throws java.lang.Exception {
        for (int i=0; i<a.length; i++) {
            if (i!=0) wr(" ");
            wr(a[i]);
        }
        wl();
    }

    void wr(double x)  throws java.lang.Exception {
        writer.write(x);
    }    

    void wr(String s)  throws java.lang.Exception {
        writer.write(s);
    }

    void wl()  throws java.lang.Exception {
        writer.writeLine();
    }

    void wline(String s)  throws java.lang.Exception {
        writer.writeLine(s);
    }

    static class Writer {
        BufferedWriter bw;

        public Writer(OutputStream out) {
            bw = new BufferedWriter(new OutputStreamWriter(out));
        }

        void write(String s) throws java.lang.Exception {
            bw.write(s);
        }

        void write(int x) throws java.lang.Exception {
            write(String.valueOf(x));
        }

        void write(long x) throws java.lang.Exception {
            write(String.valueOf(x));
        }

        void write(double x) throws java.lang.Exception {
            write(String.valueOf(x));
        }

        void write(char c) throws java.lang.Exception {
            bw.write(c);
        }

        void newLine() throws java.lang.Exception {
            bw.newLine();
        }

        void writeLine(String s) throws java.lang.Exception {
            write(s);
            newLine();
        }

        void writeLine(int n) throws java.lang.Exception {
            writeLine(String.valueOf(n));
        }

        void writeLine(long n) throws java.lang.Exception {
            writeLine(String.valueOf(n));
        }
        
        void writeLine() throws java.lang.Exception {
            writeLine("");
        }

        void close() throws java.lang.Exception {
            bw.flush();
            bw.close();
        }
    }

    static class Reader {
        BufferedReader br;
        StringTokenizer st;

        public Reader(InputStream in) {
            br = new BufferedReader(new InputStreamReader(in));
        }

        String nextToken() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        String[] nextTokens(int n) {
            String[] a = new String[n];
            for (int i=0; i<n; i++) {
                a[i] = nextToken();
            }
            return a;
        }

        int nextInt() {
            return Integer.parseInt(nextToken());
        }

        int[] nextInts(int n) {
            int[] a = new int[n];
            for (int i=0; i<n; i++) {
                a[i] = nextInt();
            }
            return a;
        }

        long nextLong() {
            return Long.parseLong(nextToken());
        }

        long[] nextLongs(int n) {
            long[] a = new long[n];
            for (int i=0; i<n; i++) {
                a[i] = nextInt();
            }
            return a;
        }

        double nextDouble() {
            return Double.parseDouble(nextToken());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

        void close() throws java.lang.Exception {
            br.close();
        }
    }
}